When plugging an external hard drive into the PS5, it’s made pretty clear that you can’t store PS5 games on an external with phrases such as “You can install PS4 games to extended storage and play them directly from there”.
We’d also like to add that, at the time of writing, it’s impossible to copy PS5 games across to an external HDD for storage purposes, meaning that you’ll have to either re-download or re-install any next-gen titles that you delete.